Geometrical Consequences of Conformal Symmetries in Gradient Schouten Solitons

Alhouiti, Noura M.; Alkhaldi, Ali H.; Ali, Akram

doi:10.3390/math14111901

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Geometrical Consequences of Conformal Symmetries in Gradient Schouten Solitons

by

Noura M. Alhouiti

¹,

Ali H. Alkhaldi

² and

Akram Ali

^2,*

¹

Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia

²

Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia

^*

Author to whom correspondence should be addressed.

Mathematics 2026, 14(11), 1901; https://doi.org/10.3390/math14111901

Submission received: 4 April 2026 / Revised: 1 May 2026 / Accepted: 26 May 2026 / Published: 29 May 2026

(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications, 2nd Edition)

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Abstract

This study explores the conformal geometry of gradient Schouten solitons characterized by constant scalar curvature, which represents a notable extension of the Einstein equation. We prove that a closed gradient Schouten soliton equipped with a non-trivial closed conformal vector is isometric to the round sphere. In the sequel, we prove that a non-compact gradient Schouten solitons admitting a non-trivial gradient conformal vector field are isometric to a Euclidean space or a warped product

I \times_{ξ} M^{m - 1}

of an interval

I

and an Einstein manifold

M^{m - 1}

provided that scalar curvature of

M^{m - 1}

is constant. Moreover, the same results are proved when the soliton vector field of the gradient Schouten soliton is divergence-free.

Keywords: gradient Schouten solitons; closed conformal vector field; divergence-free; scalar curvatures

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MDPI and ACS Style

Alhouiti, N.M.; Alkhaldi, A.H.; Ali, A. Geometrical Consequences of Conformal Symmetries in Gradient Schouten Solitons. Mathematics 2026, 14, 1901. https://doi.org/10.3390/math14111901

AMA Style

Alhouiti NM, Alkhaldi AH, Ali A. Geometrical Consequences of Conformal Symmetries in Gradient Schouten Solitons. Mathematics. 2026; 14(11):1901. https://doi.org/10.3390/math14111901

Chicago/Turabian Style

Alhouiti, Noura M., Ali H. Alkhaldi, and Akram Ali. 2026. "Geometrical Consequences of Conformal Symmetries in Gradient Schouten Solitons" Mathematics 14, no. 11: 1901. https://doi.org/10.3390/math14111901

APA Style

Alhouiti, N. M., Alkhaldi, A. H., & Ali, A. (2026). Geometrical Consequences of Conformal Symmetries in Gradient Schouten Solitons. Mathematics, 14(11), 1901. https://doi.org/10.3390/math14111901

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Geometrical Consequences of Conformal Symmetries in Gradient Schouten Solitons

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